Two Types of Updatelessness

Cross-posted.

Just a small note which I’m not sure has been men­tioned any­where else:

It seems like there are two differ­ent classes of “up­date­less rea­son­ing”.

In prob­lems like Agent Si­mu­lates Pre­dic­tor, switch­ing to up­date­less rea­son­ing is bet­ter for you in the very situ­a­tion you find your­self in. The gains ac­crue to you. You ob­jec­tively achieve higher ex­pected value, at the point of de­ci­sion, by mak­ing the de­ci­sion from the per­spec­tive of your­self long ago rather than do­ing what seems higher EV from the cur­rent per­spec­tive.

In prob­lems like coun­ter­fac­tual mug­ging, the gains do not ac­crue to the agent at the point of mak­ing the de­ci­sion. The in­crease in ex­pected value goes to other pos­si­ble selves, which the de­ci­sion-point self does not even be­lieve in any more. The claim of higher EV is quite sub­jec­tive; it de­pends en­tirely on one’s prior.

For lack of bet­ter terms, I’ll call the first type all-up­side up­date­less­ness; the sec­ond type is mixed-up­side.

It is quite pos­si­ble to con­struct de­ci­sion the­o­ries which get all-up­side up­date­less rea­son­ing with­out get­ting mixed-up­side. Asymp­totic de­ci­sion the­ory was one.

On the other hand, it seems un­likely that any nat­u­ral pro­posal would get mixed-up­side with­out get­ting the all-up­side cases. Policy se­lec­tion, for ex­am­ple, au­to­mat­i­cally gets both types (to the limited ex­tent that it en­ables up­date­less­ness rea­son­ing).

Nonethe­less, I find it plau­si­ble that one wants two differ­ent mechanisms to get the two differ­ent kinds. It seems to me that one can han­dle all-up­side cases in a more ob­jec­tive way, get­ting good over­all guaran­tees. Mixed-up­side cases, on the other hand, re­quire more messi­ness and com­pro­mise, as in the policy se­lec­tion pro­posal. So, it could be benefi­cial to com­bine a mechanism which does perfectly for all-up­side cases with a mechanism that pro­vides some weaker guaran­tee for mixed-up­side.

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